Some kind of coreset for \(k\) -means of size near-linear in \(k\)  was suggested in [1]}. However, unlike the definition of this paper, the multiplicative weights of some of the points in this coreset were (i) negative, and (ii) depends on the query, i.e., instead of a weight \(w(p)>0\)  for an input point \(p\) , as in this paper, the weight is \(w(p,C)\in \mathbb {R}\)  where \(C\)  is the set of queries. While exhaustive search was suggested to compute a PTAS for the coreset, it is not clear how to compute existing algorithms or heuristics (what is actually done in practice) on such a coreset. On the contrary, generalizing an existing approximation algorithm for the \(k\) -means problem to handle positively weights is easy, and public implementations are not hard to find (e.g. in Matlab and Python).
